Question

Which is greater 20/3 or 3 1/2

Answer 1

To compare \( \frac{20}{3} \) and \( 3 \frac{1}{2} \), let's convert \( 3 \frac{1}{2} \) into an improper fraction.

First, convert \( 3 \frac{1}{2} \):
\[
3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}
\]

Now we have:
\[
\frac{20}{3} \quad \text{and} \quad \frac{7}{2}
\]

To compare these fractions, we can find a common denominator. The least common multiple of 3 and 2 is 6.

Now, convert both fractions to have the same denominator:
1. For \( \frac{20}{3} \):
\[
\frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6}
\]

2. For \( \frac{7}{2} \):
\[
\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}
\]

Now, we compare \( \frac{40}{6} \) and \( \frac{21}{6} \):
\[
\frac{40}{6} > \frac{21}{6}
\]

Therefore, \( \frac{20}{3} \) is greater than \( 3 \frac{1}{2} \).

So:
\[
\frac{20}{3} > 3 \frac{1}{2}
\]